Floating-point error propagation in iterative methods

✍ Scribed by René Alt

• Publisher: Elsevier Science
• Year: 1988
• Tongue: English
• Weight: 923 KB
• Volume: 30
• Category: Article
• ISSN: 0378-4754
• DOI: 10.1016/0378-4754(88)90072-9

✦ Synopsis

In this paper, a formal space for the modelization of computer arithmetic and a pseudo-distance defined on this space to study computer iterative sequences is proposed.

Some properties if this pseudo-distance are examined and a termination criterion for iterative sequences in this space is given. This termination criterion applies to one-dimensional as well as multi-dimensional sequences. The necessity of an estimation of the accuracy on the last computed iterate is shown, as well as a method for doing so. Simple numerical examples are given explaining the various cases of approximation of the exact solution of a mathematical problem by the last iterate of a data processing sequence.